In this paper, we deal with the problem of optimal control of a deterministic model of hepatitis C virus （HCV）. In the first part of our analysis, a mathematical modeling of HCV dynamics which can be controlled by a...In this paper, we deal with the problem of optimal control of a deterministic model of hepatitis C virus （HCV）. In the first part of our analysis, a mathematical modeling of HCV dynamics which can be controlled by antiretroviral therapy as fixed controls has been presented and analyzed which incorporates two mechanisms： infection by free virions and the direct cell-to-cell transmission. Basic reproduction number is calculated and the existence and stability of equilibria are investigated. In the second part, the optimal control problem representing drug treatment strategies of the model is explored considering control parameters as time-dependent in order to minimize not only the population of infected cells but also the associated costs. At the end of the paper, the impact of combination of the strategies in the control of HCV and their effectiveness are compared by numerical simulation.展开更多
In this paper, we study the global dynamics of a SVEIS epidemic model with distinct incidence for exposed and infectives. The model is analyzed for stability and bifurcation behavior. To account for the realistic phen...In this paper, we study the global dynamics of a SVEIS epidemic model with distinct incidence for exposed and infectives. The model is analyzed for stability and bifurcation behavior. To account for the realistic phenomenon of non-homogeneous mixing, the effect of diffusion on different population subclasses is considered. The diffusive model is analyzed using matrix stability theory and conditions for Turing bifurcation are derived. Numerical simulations support our analytical results on the dynamic behavior of tile model.展开更多
In this paper, we investigate the dynamical behavior of a fractional order phytoplankton- zooplankton system. In this paper, stability analysis of the phytoplankton zooplankton model （PZM） is studied by using the fr...In this paper, we investigate the dynamical behavior of a fractional order phytoplankton- zooplankton system. In this paper, stability analysis of the phytoplankton zooplankton model （PZM） is studied by using the fractional Routh-Hurwitz stability conditions. We have studied the local stability of the equilibrium points of PZM. We applied an efficient numerical method based on converting the fractional derivative to integer derivative to solve the PZM.展开更多
In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton-zooplankton （TPPZ） system with nutrient cycling. We propose a mathematical system to model this situation....In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton-zooplankton （TPPZ） system with nutrient cycling. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the equilibriums are determined. Local stability analysis of the TPPZ is studied by using the fractional Routh-Hurwitz stability conditions. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.展开更多
文摘In this paper, we deal with the problem of optimal control of a deterministic model of hepatitis C virus （HCV）. In the first part of our analysis, a mathematical modeling of HCV dynamics which can be controlled by antiretroviral therapy as fixed controls has been presented and analyzed which incorporates two mechanisms： infection by free virions and the direct cell-to-cell transmission. Basic reproduction number is calculated and the existence and stability of equilibria are investigated. In the second part, the optimal control problem representing drug treatment strategies of the model is explored considering control parameters as time-dependent in order to minimize not only the population of infected cells but also the associated costs. At the end of the paper, the impact of combination of the strategies in the control of HCV and their effectiveness are compared by numerical simulation.
文摘In this paper, we study the global dynamics of a SVEIS epidemic model with distinct incidence for exposed and infectives. The model is analyzed for stability and bifurcation behavior. To account for the realistic phenomenon of non-homogeneous mixing, the effect of diffusion on different population subclasses is considered. The diffusive model is analyzed using matrix stability theory and conditions for Turing bifurcation are derived. Numerical simulations support our analytical results on the dynamic behavior of tile model.
文摘In this paper, we investigate the dynamical behavior of a fractional order phytoplankton- zooplankton system. In this paper, stability analysis of the phytoplankton zooplankton model （PZM） is studied by using the fractional Routh-Hurwitz stability conditions. We have studied the local stability of the equilibrium points of PZM. We applied an efficient numerical method based on converting the fractional derivative to integer derivative to solve the PZM.
文摘In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton-zooplankton （TPPZ） system with nutrient cycling. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the equilibriums are determined. Local stability analysis of the TPPZ is studied by using the fractional Routh-Hurwitz stability conditions. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.
